Research Summary
My research interests are spread broadly across the fields of analytic number theory, combinatorics, and probability. I am particularly interested in the distribution of prime numbers, and in the local statistics of point sequences.
​
A formal research statement is available here.
I've also written a non-technical summary here.
​
​
​
Preprints
Effective results on the size and structure of sumsets (j/w/ Andrew Granville and George Shakan)
​
Published
Correlations of sieve weights and distributions of zeros
International Journal of Number Theory, 9(1),139-167, 2023
​
On the triple correlations of fractional parts of $n^2\alpha$ (j/w/ Niclas Technau)
Canadian Journal of Mathematics. 74(5),1347–1384, 2022
​
A tight structure theorem for sumsets (j/w/ Andrew Granville)
Proceedings of the American Mathematical Society, 149(10), 4073-4082, 2021
​
Extremal problems for GCDs (j/w/ Ben Green)
Combinatorics, Probability and Computing, 30(6), 922-929, 2021
​
Gowers norms control Diophantine inequalities
arXiv:1703.00885
Arithmetic progressions with restricted digits (j/w Alexander Walker)
GCD sums and sum-product estimates (j/w Thomas F. Bloom)
Additive energy and the metric Poissonian property (j/w Thomas F. Bloom, Sam Chow, Ayla Gafni)
The primes are not metric Poissonian
arXiv:1702.07365
A footnote in parity breaking (j/w Olivier Ramare)
arXiv:1610.05804
A multiplicative analogue of Schnirelmann's theorem
arXiv:1505.03328
Bull. London Math. Soc., 48 (6),1018-1028, 2016.